The subject disclosure relates to quantum circuits, e.g., quantum circuit design. Quantum computing employs quantum physics to encode and process information, rather than binary digital techniques based on transistors. A quantum computing device employs quantum bits (also referred to as qubits) that operate according to the laws of quantum physics and can exhibit phenomena such as superposition and entanglement. The superposition principle of quantum physics allows qubits to be in a state that partially represent both a value of “1” and a value of “0” at the same time. The entanglement principle of quantum physics allows qubits to be correlated with each other such that the combined states of the qubits cannot be factored into individual qubit states. For instance, a state of a first qubit can depend on a state of a second qubit. As such, a quantum circuit can employ qubits to encode and process information in a manner that can be significantly different from binary digital techniques based on transistors. However, the designing of quantum circuits often can be relatively difficult and/or time consuming.
With regard to quantum circuit design, a conventional approach can use a universal quantum computing circuit that can be utilized for virtually all types of algorithms. The universal quantum computing circuit typically can have qubits that can be connected to all of their neighbor qubits, and typically can run all or virtually all types of algorithms, although with varying and/or limited levels of performance, due at least in part to, for example, resource limits and design constraints, as well as the universal nature of the connectivity of the qubits in the universal quantum computing circuit.
Another conventional approach to improving the operation of quantum circuits involves identifying two-qubit operations (corresponding to one or more two-qubit gates) in a circuit and trying to simplify them. One way to simplify a gate is to either approximate or expand the two-qubit gate by different processes. Universal gates can be used to expand the gates to be simplified, though because of their varying and/or limited levels of performance, their use often does not simplify a circuit.
An example of a universal gate that is known to be able to simplify some two-qubit gates is a super controlled gate. Any operation on two-qubits can be implemented using at most three super controlled gates. Operations on two-qubits can also be termed Special Unitary (4) operations (SU(4)). One type of super controlled gate is the controlled NOT (CNOT) gate and it is known that, as a super controlled gate, any operation on two-qubits can be implemented using zero or at most three CNOT gates.
With these known approaches to improving the operation of quantum circuits however, there are problems. The conventional approaches noted above only use a discrete single-qubit basis set for expanding expressions. Based on this limited basis set, these approaches have a problem accurately handling a variety of different expressions without significant inaccuracy. These approaches also do not perform simplification operations while considering performance problems that can result from the use of certain two-qubit gates, e.g., they fail to consider problems with inaccuracies that can result from the use of certain two-qubit gates and/or certain numbers of the same two-qubit gates. These and other problems of conventional quantum computing circuit design approaches can result in inaccuracies as well as inefficient and/or ineffective circuits and/or inefficient performance of a quantum circuit design.